Sunday, 4 December 2011

Arithmetic Mean (ungroup data & group data)

The sum of all values in the series divided by the total numbers of values in the series.

The method of Arithmetic mean is also known as:

-Arithmetic mean

-Mean

-Simple mean

-Average

-Mean by direct method

Arithmetic Mean (ungroup-data)

Formula:

Mean = sum of elements / number of elements

= a1+a2+a3+.....+an/n

Arithmetic Mean= ΣX/n

where

X = Individual value

n = Total number of values

Example: To find the mean of 3,5,7.

Step 1: Find the sum of the numbers.

3+5+7 = 15

Step 2:Calculate the total number.

there are 3 numbers.

Step 3:Finding mean.

15/3 = 5Ans = 5

Arithmetic Mean (group-data) :

Formula:

Arithmetic Mean= ΣfX/Σf

where

X = Individual value

f = Frequency

Grouped Data Arithmetic Mean Example:.

X -ValueFrequency(f)ΣfX

121 * 2 = 2

232 * 3 = 6

323 * 2 = 6

Σf = 7ΣfX= 14

Step 1: Find Σf.

Σf = 7

Step 2:Now, find ΣfX.

ΣfX = 14

Step 3: Now, Substitute in the above formula given

Arithmetic mean = ΣfX/Σf = 14/7 = 2

Example:.

ClassesFrequency

of Class

Age (years)f

0--- 56

5--- 1012

10 ---1519

15 ---203

Total

Find Arithmetic mean for given data.

As the formula forA.M (Group data) = ΣfX/Σf

So we need“X” first

ClassesFrequencyMid Point

of Class

Age (years)fXfX

0--- 562.515

5--- 10127.590

10 ---151912.5237.5

15 ---20317.552.5

Total40395

Note: [In this example we have already class boundary, Ifclass boundary not given to find A.M then no problem and we will not make class boundary. Class boundary is required only forMedian, Mode, Quartile, Decile, Percentile